InterviewSolution
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InterviewSolution
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The domain of definition of the function`f(x)=sqrt(sin^(-1)(2x)+pi/6)`for real-valued `x`isA. `[-(1)/(4),(1)/(2)]`B. `[-(1)/(2),(1)/(2)]`C. `(-(1)/(2),(1)/(9))`D. `[-(1)/(4),(1)/(4)]` |
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Answer» Correct Answer - A Here, `f(x)=sqrt(sin^(-1)(2x)+(pi)/(6))`, to find domain we must have, `sin^(-1)(2x)+(pi)/(6) ge 0 " "["but "-(pi)/(2) le sin^(-1)theta le (pi)/(2)]` ` -(pi)/(6) le sin^(-1) (2x) le (pi)/(2)` `sin(-(pi)/(6)) le 2x le "sin"(pi)/(2) rArr (-1)/(2) le 2x le (1)/(2)` `(-1)/(4) le x le (1)/(2)` `because x in [(-1)/(4), (1)/(2)]` |
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